Assertion (A) : is continuous at for . Reason (R) : For a function to be continuous…

MATHEMATICS · Subjective · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Assertion (A) : f(x)={3x−8,x≤52k,x>5f(x) = \begin{cases} 3x - 8, & x \le 5 \\ 2k, & x > 5 \end{cases} is continuous at x=5x = 5 for k=52k = \frac{5}{2} . Reason (R) : For a function ff to be continuous at x=ax = a , lim⁡x→a−f(x)=lim⁡x→a+f(x)=f(a).\lim_{x \to a^-} f(x) = \lim_{x \to a^+} f(x) = f(a). (A) Both Assertion (A) and Reason (R) are true and the Reason (R) is the correct explanation of the Assertion (A). (B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A). (C) Assertion (A) is true, but Reason (R) is false. (D) Assertion (A) is false, but Reason (R) is true.

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